Another Look At Counting By Weighing

    Authors

    D. M. Nickerson

    Comments

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    Abbreviated Journal Title

    Commun. Stat.-Simul. Comput.

    Keywords

    Coefficient Of Variation; Renewal Theory; Overshoot Correction; Sequential Sampling Rule; Renewal Theory; Statistics & Probability

    Abstract

    In many instances a fixed number of items, N, must be obtained from a large collection of these items. The process of counting out these items, however, becomes impractical if N is quite large. An alternative to individually counting out N items is counting by weighing. If the mean weight of an individual item, mu, is known, then we simply assemble a batch that weighs Nmu. If the mean weight is unknown, then we take an initial sample of size n, much less than N, from which an estimate, m, of the mean weight is obtained. We then assemble a batch that weighs (N - n)m. This procedure leads in principle to a set of N total items (n counted, N - n weighed). By way of renewal theory, this article examines the distributional properties of the actual number of items in the batch. Further, from the distributional properties of the actual number of items counted, this article addresses the problem of determining the smallest initial sample size n for estimating N to within some specified bound with high probability. Also, refinements known as ''overshoot'' and ''continuity'' corrections are implemented to improve the procedure. Finally, a simulation study was performed to evaluate the performance of the procedure.

    Journal Title

    Communications in Statistics-Simulation and Computation

    Volume

    22

    Issue/Number

    2

    Publication Date

    1-1-1993

    Document Type

    Article

    Language

    English

    First Page

    323

    Last Page

    343

    WOS Identifier

    WOS:A1993KZ56600002

    ISSN

    0361-0918

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